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Homological mirror symmetry for Calabi-Yau hypersurfaces in projective space. (English) Zbl 1344.53073
This review is based on the abstract of the paper:
Its objective is to prove the Homological Mirror Symmetry for a smooth \(d\)-dimensional Calabi-Yau hypersurface in projective space for any \(d\geq 3\). The main ingredients for the the proof are the following:
(1)
The construction of an immersed Lagrangian sphere in a \(d\)-dimensional pair of pants.
(2)
The introduction of the relative Fukaya category and an understanding of its grading structure.
(3)
A description of the behaviour of this category with respect to branched covers via an orbifold Fukaya category.
(4)
A Morse-Bott model for the relative Fukaya category that allows one to make explicit computations.
(5)
The introduction of certain graded categories of matrix factorizations mirror to the relative Fukaya category.

MSC:
53D37 Symplectic aspects of mirror symmetry, homological mirror symmetry, and Fukaya category
14J33 Mirror symmetry (algebro-geometric aspects)
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